Geek Challenge: The Perfect Bracket

With March Madness wrapping up and everyone’s brackets broken once again, this month’s Geek Challenge is about what it might take to build the perfect bracket. It's time for all the mathletes out there to show off their skills.

Imagine that for every game in the NCAA tournament you know the probability p for the favored team to win the game. For simplicity’s sake, let’s assume p is the same for all the games in the tournament.

You fill out your bracket to reflect these odds 50 times over 50 years (p is the same every year). How large does p need to be for there to be a 50% chance that one of your 50 brackets was a perfect bracket?

A: 65.344%

B: 87.481%

C: 93.424%

D: 98.637%

E: 99.998%

Extra credit for a general formula for p in terms of the number of brackets filled out and the probability that one of those brackets is a perfect bracket.

The solution with the most complete analysis will be this month's Geek Challenge winner!

Submit responses to geekchallenge@dmcinfo.com by May 5, 2017.

Check out any previous Geek Challenges you might have missed!